Traveling to Kullu Manali is possible throughout the year. But it all depends on your requirement as what exactly you are looking for your Holidays.
If you are keen to see snowfall and enjoy some snow activities with your family and friends, November to March is the best time to visit Manali. Some tourist places in Manali like Rohtang Pass (and sometimes Solang Valley too) gets disconnected from the city.
You cannot enjoy some adventure activities like River Rafting. Water is so chilled that you cannot get into it for a single minute.
If you want to enjoy The actual scenic beauty, Greenery all over, August to November mid is the best time. You can also visit Rohtang Pass during this period.
Apr to July mid is the season time - Too much crowd and traffic, so no comments (Personal Choice).
July and Aug is a Rainy season, Though good again to enjoy greenery with rains.

There is no direct flight from Mumbai to Manali. In fact from any City to Manali (Except Delhi and Chandigarh).
Air India is the only Direct Flight to Manali is only from Delhi and Chandigarh and that too operates occasionally.

There is no Train track to Kullu Manali. You cannot go directly from Delhi to Manali on Train.

If you are planning to travel by train from Delhi or any other city. You have to go get down at Chandigarh. From there you can catch Volvo bus to Manali or hire a car for complete trip.

You can also get down at Joginder Nagar and from there you can hire a car as well.

Reaching Kalka is a bit off the way. If you are planning for Shimla and Manali tour then reaching Kalka is a very good option. You can go Shimla by Toy train and then after staying at Shimla you can proceed to Manali. In return, you can get down at Chandigarh or Delhi.

Kullu Manali is far far better than Shimla.
Shimla is overcrowded and expensive as compare to Kullu Manali. Shimla Roads are congested, have fewer tourist places to visit as compared to Manali.
Delhi to Shimla distance is 375 km It takes 8 Hrs to reach Shimla from Delhi.
Whereas Kullu Manali is 580 km from Delhi. It takes around 13 Hours to reach Manali from Delhi and 9 Hrs from Chandigarh.

Manali doesn't have an airport. The nearest Airport to Manali is BHUNTAR. Located 50 km before Manali and 10 km before Kullu.
There is no direct flight from any City, except Delhi and Chandigarh.
From Delhi to Kullu Flights are daily. Flights are on alternate days.
Flight Cost Rs 10000 Per Person One Way (Aprox).